Certification Problem
Input (TPDB SRS_Standard/ICFP_2010/157593)
The rewrite relation of the following TRS is considered.
|
0(0(0(1(x1)))) |
→ |
0(1(0(0(2(3(x1)))))) |
(1) |
|
0(0(4(1(x1)))) |
→ |
4(2(0(1(0(x1))))) |
(2) |
|
0(0(4(1(x1)))) |
→ |
0(2(1(4(2(0(x1)))))) |
(3) |
|
0(0(4(1(x1)))) |
→ |
1(0(5(4(2(0(x1)))))) |
(4) |
|
0(0(4(1(x1)))) |
→ |
3(4(2(0(1(0(x1)))))) |
(5) |
|
0(3(4(0(x1)))) |
→ |
0(3(0(2(4(2(x1)))))) |
(6) |
|
0(3(4(0(x1)))) |
→ |
0(3(4(2(0(2(x1)))))) |
(7) |
|
0(3(4(0(x1)))) |
→ |
0(4(5(3(0(5(x1)))))) |
(8) |
|
0(4(4(0(x1)))) |
→ |
4(4(2(0(0(x1))))) |
(9) |
|
0(4(4(0(x1)))) |
→ |
0(4(0(2(4(2(x1)))))) |
(10) |
|
0(4(4(0(x1)))) |
→ |
4(2(0(0(2(4(x1)))))) |
(11) |
|
0(4(4(0(x1)))) |
→ |
4(2(0(0(4(2(x1)))))) |
(12) |
|
0(4(4(0(x1)))) |
→ |
4(2(0(4(2(0(x1)))))) |
(13) |
|
0(4(4(1(x1)))) |
→ |
0(1(4(4(2(x1))))) |
(14) |
|
0(4(4(1(x1)))) |
→ |
1(4(4(2(0(x1))))) |
(15) |
|
0(4(4(1(x1)))) |
→ |
0(1(4(4(2(3(x1)))))) |
(16) |
|
0(4(4(1(x1)))) |
→ |
0(1(5(4(4(2(x1)))))) |
(17) |
|
0(4(4(1(x1)))) |
→ |
1(5(4(4(2(0(x1)))))) |
(18) |
|
0(4(4(1(x1)))) |
→ |
2(4(0(1(5(4(x1)))))) |
(19) |
|
0(4(4(1(x1)))) |
→ |
2(4(4(1(2(0(x1)))))) |
(20) |
|
0(4(4(1(x1)))) |
→ |
2(4(5(4(0(1(x1)))))) |
(21) |
|
0(4(4(1(x1)))) |
→ |
4(2(4(2(1(0(x1)))))) |
(22) |
|
1(4(4(0(x1)))) |
→ |
5(4(4(2(0(1(x1)))))) |
(23) |
|
1(4(4(1(x1)))) |
→ |
2(1(4(1(2(4(x1)))))) |
(24) |
|
1(4(4(1(x1)))) |
→ |
2(3(4(1(4(1(x1)))))) |
(25) |
|
1(4(4(1(x1)))) |
→ |
2(4(1(2(1(4(x1)))))) |
(26) |
|
1(4(4(1(x1)))) |
→ |
2(4(2(1(4(1(x1)))))) |
(27) |
|
4(0(0(0(x1)))) |
→ |
0(4(2(0(0(5(x1)))))) |
(28) |
|
4(0(0(1(x1)))) |
→ |
2(3(0(1(0(4(x1)))))) |
(29) |
|
4(0(4(0(x1)))) |
→ |
2(4(2(0(0(4(x1)))))) |
(30) |
|
4(0(4(0(x1)))) |
→ |
3(4(2(0(4(0(x1)))))) |
(31) |
|
4(0(4(1(x1)))) |
→ |
2(4(2(0(4(1(x1)))))) |
(32) |
|
4(3(4(0(x1)))) |
→ |
4(0(3(4(2(x1))))) |
(33) |
|
4(3(4(0(x1)))) |
→ |
4(4(2(0(3(x1))))) |
(34) |
|
4(3(4(0(x1)))) |
→ |
0(4(2(3(4(2(x1)))))) |
(35) |
|
4(3(4(0(x1)))) |
→ |
2(3(0(4(4(5(x1)))))) |
(36) |
|
4(3(4(0(x1)))) |
→ |
2(3(4(4(0(2(x1)))))) |
(37) |
|
4(3(4(0(x1)))) |
→ |
2(4(0(3(4(2(x1)))))) |
(38) |
|
4(3(4(0(x1)))) |
→ |
4(2(0(4(2(3(x1)))))) |
(39) |
|
4(3(4(0(x1)))) |
→ |
4(3(0(5(4(2(x1)))))) |
(40) |
|
4(3(4(0(x1)))) |
→ |
4(4(2(3(0(2(x1)))))) |
(41) |
|
4(3(4(0(x1)))) |
→ |
4(4(5(3(0(3(x1)))))) |
(42) |
|
4(3(4(1(x1)))) |
→ |
3(4(2(4(1(x1))))) |
(43) |
|
4(3(4(1(x1)))) |
→ |
1(4(2(4(2(3(x1)))))) |
(44) |
|
4(3(4(1(x1)))) |
→ |
2(3(1(4(5(4(x1)))))) |
(45) |
|
4(3(4(1(x1)))) |
→ |
2(3(4(2(1(4(x1)))))) |
(46) |
|
4(3(4(1(x1)))) |
→ |
2(4(2(3(1(4(x1)))))) |
(47) |
|
4(3(4(1(x1)))) |
→ |
3(1(4(2(4(2(x1)))))) |
(48) |
|
4(3(4(1(x1)))) |
→ |
3(4(2(4(5(1(x1)))))) |
(49) |
|
4(3(4(1(x1)))) |
→ |
3(4(5(3(4(1(x1)))))) |
(50) |
|
4(4(4(0(x1)))) |
→ |
2(4(2(4(4(0(x1)))))) |
(51) |
|
4(4(4(1(x1)))) |
→ |
2(4(2(4(1(4(x1)))))) |
(52) |
|
4(4(4(1(x1)))) |
→ |
4(2(4(1(2(4(x1)))))) |
(53) |
|
4(4(4(1(x1)))) |
→ |
4(5(4(1(5(4(x1)))))) |
(54) |
|
0(0(4(0(0(x1))))) |
→ |
0(4(2(0(0(0(x1)))))) |
(55) |
|
0(1(3(5(0(x1))))) |
→ |
0(1(3(0(5(3(x1)))))) |
(56) |
|
0(3(4(0(0(x1))))) |
→ |
3(4(2(0(0(0(x1)))))) |
(57) |
|
0(3(5(0(1(x1))))) |
→ |
0(1(0(5(2(3(x1)))))) |
(58) |
|
0(3(5(4(1(x1))))) |
→ |
5(1(0(4(5(3(x1)))))) |
(59) |
|
0(4(3(4(0(x1))))) |
→ |
0(2(3(4(4(0(x1)))))) |
(60) |
|
1(4(4(0(0(x1))))) |
→ |
4(1(4(2(0(0(x1)))))) |
(61) |
|
1(4(4(0(1(x1))))) |
→ |
1(4(4(1(2(0(x1)))))) |
(62) |
|
1(4(4(4(1(x1))))) |
→ |
2(4(1(4(4(1(x1)))))) |
(63) |
|
4(0(0(4(1(x1))))) |
→ |
4(4(2(0(1(0(x1)))))) |
(64) |
|
4(0(4(4(0(x1))))) |
→ |
4(0(4(2(4(0(x1)))))) |
(65) |
|
4(1(0(0(1(x1))))) |
→ |
4(2(0(1(1(0(x1)))))) |
(66) |
|
4(1(3(4(0(x1))))) |
→ |
3(1(4(2(4(0(x1)))))) |
(67) |
|
4(3(1(0(0(x1))))) |
→ |
1(4(2(3(0(0(x1)))))) |
(68) |
|
4(3(1(0(0(x1))))) |
→ |
3(1(4(2(0(0(x1)))))) |
(69) |
|
4(3(1(5(0(x1))))) |
→ |
1(4(5(3(0(1(x1)))))) |
(70) |
|
4(3(2(4(0(x1))))) |
→ |
4(2(0(3(4(2(x1)))))) |
(71) |
|
4(3(4(4(1(x1))))) |
→ |
4(4(3(1(4(2(x1)))))) |
(72) |
|
4(3(5(0(0(x1))))) |
→ |
4(0(5(2(3(0(x1)))))) |
(73) |
|
4(3(5(0(1(x1))))) |
→ |
2(3(5(4(0(1(x1)))))) |
(74) |
|
4(3(5(4(0(x1))))) |
→ |
0(3(4(5(4(5(x1)))))) |
(75) |
|
4(3(5(4(0(x1))))) |
→ |
0(4(5(3(4(2(x1)))))) |
(76) |
|
4(3(5(4(0(x1))))) |
→ |
4(4(5(3(0(2(x1)))))) |
(77) |
|
4(3(5(4(0(x1))))) |
→ |
5(4(3(4(2(0(x1)))))) |
(78) |
|
4(3(5(4(1(x1))))) |
→ |
3(4(2(4(5(1(x1)))))) |
(79) |
|
4(3(5(5(0(x1))))) |
→ |
0(2(3(5(4(5(x1)))))) |
(80) |
|
4(3(5(5(1(x1))))) |
→ |
1(5(4(2(5(3(x1)))))) |
(81) |
|
4(4(0(0(1(x1))))) |
→ |
4(0(4(2(0(1(x1)))))) |
(82) |
|
4(4(4(4(1(x1))))) |
→ |
4(4(4(1(2(4(x1)))))) |
(83) |
|
4(4(5(0(1(x1))))) |
→ |
4(5(0(1(4(2(x1)))))) |
(84) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by matchbox @ termCOMP 2023)
1 String Reversal
Since only unary symbols occur, one can reverse all terms and obtains the TRS
|
1(0(0(0(x1)))) |
→ |
3(2(0(0(1(0(x1)))))) |
(85) |
|
1(4(0(0(x1)))) |
→ |
0(1(0(2(4(x1))))) |
(86) |
|
1(4(0(0(x1)))) |
→ |
0(2(4(1(2(0(x1)))))) |
(87) |
|
1(4(0(0(x1)))) |
→ |
0(2(4(5(0(1(x1)))))) |
(88) |
|
1(4(0(0(x1)))) |
→ |
0(1(0(2(4(3(x1)))))) |
(89) |
|
0(4(3(0(x1)))) |
→ |
2(4(2(0(3(0(x1)))))) |
(90) |
|
0(4(3(0(x1)))) |
→ |
2(0(2(4(3(0(x1)))))) |
(91) |
|
0(4(3(0(x1)))) |
→ |
5(0(3(5(4(0(x1)))))) |
(92) |
|
0(4(4(0(x1)))) |
→ |
0(0(2(4(4(x1))))) |
(93) |
|
0(4(4(0(x1)))) |
→ |
2(4(2(0(4(0(x1)))))) |
(94) |
|
0(4(4(0(x1)))) |
→ |
4(2(0(0(2(4(x1)))))) |
(11) |
|
0(4(4(0(x1)))) |
→ |
2(4(0(0(2(4(x1)))))) |
(95) |
|
0(4(4(0(x1)))) |
→ |
0(2(4(0(2(4(x1)))))) |
(96) |
|
1(4(4(0(x1)))) |
→ |
2(4(4(1(0(x1))))) |
(97) |
|
1(4(4(0(x1)))) |
→ |
0(2(4(4(1(x1))))) |
(98) |
|
1(4(4(0(x1)))) |
→ |
3(2(4(4(1(0(x1)))))) |
(99) |
|
1(4(4(0(x1)))) |
→ |
2(4(4(5(1(0(x1)))))) |
(100) |
|
1(4(4(0(x1)))) |
→ |
0(2(4(4(5(1(x1)))))) |
(101) |
|
1(4(4(0(x1)))) |
→ |
4(5(1(0(4(2(x1)))))) |
(102) |
|
1(4(4(0(x1)))) |
→ |
0(2(1(4(4(2(x1)))))) |
(103) |
|
1(4(4(0(x1)))) |
→ |
1(0(4(5(4(2(x1)))))) |
(104) |
|
1(4(4(0(x1)))) |
→ |
0(1(2(4(2(4(x1)))))) |
(105) |
|
0(4(4(1(x1)))) |
→ |
1(0(2(4(4(5(x1)))))) |
(106) |
|
1(4(4(1(x1)))) |
→ |
4(2(1(4(1(2(x1)))))) |
(107) |
|
1(4(4(1(x1)))) |
→ |
1(4(1(4(3(2(x1)))))) |
(108) |
|
1(4(4(1(x1)))) |
→ |
4(1(2(1(4(2(x1)))))) |
(109) |
|
1(4(4(1(x1)))) |
→ |
1(4(1(2(4(2(x1)))))) |
(110) |
|
0(0(0(4(x1)))) |
→ |
5(0(0(2(4(0(x1)))))) |
(111) |
|
1(0(0(4(x1)))) |
→ |
4(0(1(0(3(2(x1)))))) |
(112) |
|
0(4(0(4(x1)))) |
→ |
4(0(0(2(4(2(x1)))))) |
(113) |
|
0(4(0(4(x1)))) |
→ |
0(4(0(2(4(3(x1)))))) |
(114) |
|
1(4(0(4(x1)))) |
→ |
1(4(0(2(4(2(x1)))))) |
(115) |
|
0(4(3(4(x1)))) |
→ |
2(4(3(0(4(x1))))) |
(116) |
|
0(4(3(4(x1)))) |
→ |
3(0(2(4(4(x1))))) |
(117) |
|
0(4(3(4(x1)))) |
→ |
2(4(3(2(4(0(x1)))))) |
(118) |
|
0(4(3(4(x1)))) |
→ |
5(4(4(0(3(2(x1)))))) |
(119) |
|
0(4(3(4(x1)))) |
→ |
2(0(4(4(3(2(x1)))))) |
(120) |
|
0(4(3(4(x1)))) |
→ |
2(4(3(0(4(2(x1)))))) |
(121) |
|
0(4(3(4(x1)))) |
→ |
3(2(4(0(2(4(x1)))))) |
(122) |
|
0(4(3(4(x1)))) |
→ |
2(4(5(0(3(4(x1)))))) |
(123) |
|
0(4(3(4(x1)))) |
→ |
2(0(3(2(4(4(x1)))))) |
(124) |
|
0(4(3(4(x1)))) |
→ |
3(0(3(5(4(4(x1)))))) |
(125) |
|
1(4(3(4(x1)))) |
→ |
1(4(2(4(3(x1))))) |
(126) |
|
1(4(3(4(x1)))) |
→ |
3(2(4(2(4(1(x1)))))) |
(127) |
|
1(4(3(4(x1)))) |
→ |
4(5(4(1(3(2(x1)))))) |
(128) |
|
1(4(3(4(x1)))) |
→ |
4(1(2(4(3(2(x1)))))) |
(129) |
|
1(4(3(4(x1)))) |
→ |
4(1(3(2(4(2(x1)))))) |
(130) |
|
1(4(3(4(x1)))) |
→ |
2(4(2(4(1(3(x1)))))) |
(131) |
|
1(4(3(4(x1)))) |
→ |
1(5(4(2(4(3(x1)))))) |
(132) |
|
1(4(3(4(x1)))) |
→ |
1(4(3(5(4(3(x1)))))) |
(133) |
|
0(4(4(4(x1)))) |
→ |
0(4(4(2(4(2(x1)))))) |
(134) |
|
1(4(4(4(x1)))) |
→ |
4(1(4(2(4(2(x1)))))) |
(135) |
|
1(4(4(4(x1)))) |
→ |
4(2(1(4(2(4(x1)))))) |
(136) |
|
1(4(4(4(x1)))) |
→ |
4(5(1(4(5(4(x1)))))) |
(137) |
|
0(0(4(0(0(x1))))) |
→ |
0(0(0(2(4(0(x1)))))) |
(138) |
|
0(5(3(1(0(x1))))) |
→ |
3(5(0(3(1(0(x1)))))) |
(139) |
|
0(0(4(3(0(x1))))) |
→ |
0(0(0(2(4(3(x1)))))) |
(140) |
|
1(0(5(3(0(x1))))) |
→ |
3(2(5(0(1(0(x1)))))) |
(141) |
|
1(4(5(3(0(x1))))) |
→ |
3(5(4(0(1(5(x1)))))) |
(142) |
|
0(4(3(4(0(x1))))) |
→ |
0(4(4(3(2(0(x1)))))) |
(143) |
|
0(0(4(4(1(x1))))) |
→ |
0(0(2(4(1(4(x1)))))) |
(144) |
|
1(0(4(4(1(x1))))) |
→ |
0(2(1(4(4(1(x1)))))) |
(145) |
|
1(4(4(4(1(x1))))) |
→ |
1(4(4(1(4(2(x1)))))) |
(146) |
|
1(4(0(0(4(x1))))) |
→ |
0(1(0(2(4(4(x1)))))) |
(147) |
|
0(4(4(0(4(x1))))) |
→ |
0(4(2(4(0(4(x1)))))) |
(148) |
|
1(0(0(1(4(x1))))) |
→ |
0(1(1(0(2(4(x1)))))) |
(149) |
|
0(4(3(1(4(x1))))) |
→ |
0(4(2(4(1(3(x1)))))) |
(150) |
|
0(0(1(3(4(x1))))) |
→ |
0(0(3(2(4(1(x1)))))) |
(151) |
|
0(0(1(3(4(x1))))) |
→ |
0(0(2(4(1(3(x1)))))) |
(152) |
|
0(5(1(3(4(x1))))) |
→ |
1(0(3(5(4(1(x1)))))) |
(153) |
|
0(4(2(3(4(x1))))) |
→ |
2(4(3(0(2(4(x1)))))) |
(154) |
|
1(4(4(3(4(x1))))) |
→ |
2(4(1(3(4(4(x1)))))) |
(155) |
|
0(0(5(3(4(x1))))) |
→ |
0(3(2(5(0(4(x1)))))) |
(156) |
|
1(0(5(3(4(x1))))) |
→ |
1(0(4(5(3(2(x1)))))) |
(157) |
|
0(4(5(3(4(x1))))) |
→ |
5(4(5(4(3(0(x1)))))) |
(158) |
|
0(4(5(3(4(x1))))) |
→ |
2(4(3(5(4(0(x1)))))) |
(159) |
|
0(4(5(3(4(x1))))) |
→ |
2(0(3(5(4(4(x1)))))) |
(160) |
|
0(4(5(3(4(x1))))) |
→ |
0(2(4(3(4(5(x1)))))) |
(161) |
|
1(4(5(3(4(x1))))) |
→ |
1(5(4(2(4(3(x1)))))) |
(162) |
|
0(5(5(3(4(x1))))) |
→ |
5(4(5(3(2(0(x1)))))) |
(163) |
|
1(5(5(3(4(x1))))) |
→ |
3(5(2(4(5(1(x1)))))) |
(164) |
|
1(0(0(4(4(x1))))) |
→ |
1(0(2(4(0(4(x1)))))) |
(165) |
|
1(4(4(4(4(x1))))) |
→ |
4(2(1(4(4(4(x1)))))) |
(166) |
|
1(0(5(4(4(x1))))) |
→ |
2(4(1(0(5(4(x1)))))) |
(167) |
1.1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
There are 135 ruless (increase limit for explicit display).
1.1.1 Monotonic Reduction Pair Processor with Usable Rules
Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
| [5(x1)] |
= |
x1 +
|
| [4(x1)] |
= |
x1 +
|
| [3(x1)] |
= |
x1 +
|
| [2(x1)] |
= |
x1 +
|
| [1(x1)] |
= |
x1 +
|
| [0(x1)] |
= |
x1 +
|
| [1#(x1)] |
= |
x1 +
|
| [0#(x1)] |
= |
x1 +
|
together with the usable
rules
|
1(0(0(0(x1)))) |
→ |
3(2(0(0(1(0(x1)))))) |
(85) |
|
1(4(0(0(x1)))) |
→ |
0(1(0(2(4(x1))))) |
(86) |
|
1(4(0(0(x1)))) |
→ |
0(2(4(1(2(0(x1)))))) |
(87) |
|
1(4(0(0(x1)))) |
→ |
0(2(4(5(0(1(x1)))))) |
(88) |
|
1(4(0(0(x1)))) |
→ |
0(1(0(2(4(3(x1)))))) |
(89) |
|
0(4(3(0(x1)))) |
→ |
2(4(2(0(3(0(x1)))))) |
(90) |
|
0(4(3(0(x1)))) |
→ |
2(0(2(4(3(0(x1)))))) |
(91) |
|
0(4(3(0(x1)))) |
→ |
5(0(3(5(4(0(x1)))))) |
(92) |
|
0(4(4(0(x1)))) |
→ |
0(0(2(4(4(x1))))) |
(93) |
|
0(4(4(0(x1)))) |
→ |
2(4(2(0(4(0(x1)))))) |
(94) |
|
0(4(4(0(x1)))) |
→ |
4(2(0(0(2(4(x1)))))) |
(11) |
|
0(4(4(0(x1)))) |
→ |
2(4(0(0(2(4(x1)))))) |
(95) |
|
0(4(4(0(x1)))) |
→ |
0(2(4(0(2(4(x1)))))) |
(96) |
|
1(4(4(0(x1)))) |
→ |
2(4(4(1(0(x1))))) |
(97) |
|
1(4(4(0(x1)))) |
→ |
0(2(4(4(1(x1))))) |
(98) |
|
1(4(4(0(x1)))) |
→ |
3(2(4(4(1(0(x1)))))) |
(99) |
|
1(4(4(0(x1)))) |
→ |
2(4(4(5(1(0(x1)))))) |
(100) |
|
1(4(4(0(x1)))) |
→ |
0(2(4(4(5(1(x1)))))) |
(101) |
|
1(4(4(0(x1)))) |
→ |
4(5(1(0(4(2(x1)))))) |
(102) |
|
1(4(4(0(x1)))) |
→ |
0(2(1(4(4(2(x1)))))) |
(103) |
|
1(4(4(0(x1)))) |
→ |
1(0(4(5(4(2(x1)))))) |
(104) |
|
1(4(4(0(x1)))) |
→ |
0(1(2(4(2(4(x1)))))) |
(105) |
|
0(4(4(1(x1)))) |
→ |
1(0(2(4(4(5(x1)))))) |
(106) |
|
1(4(4(1(x1)))) |
→ |
4(2(1(4(1(2(x1)))))) |
(107) |
|
1(4(4(1(x1)))) |
→ |
1(4(1(4(3(2(x1)))))) |
(108) |
|
1(4(4(1(x1)))) |
→ |
4(1(2(1(4(2(x1)))))) |
(109) |
|
1(4(4(1(x1)))) |
→ |
1(4(1(2(4(2(x1)))))) |
(110) |
|
0(0(0(4(x1)))) |
→ |
5(0(0(2(4(0(x1)))))) |
(111) |
|
1(0(0(4(x1)))) |
→ |
4(0(1(0(3(2(x1)))))) |
(112) |
|
0(4(0(4(x1)))) |
→ |
4(0(0(2(4(2(x1)))))) |
(113) |
|
0(4(0(4(x1)))) |
→ |
0(4(0(2(4(3(x1)))))) |
(114) |
|
1(4(0(4(x1)))) |
→ |
1(4(0(2(4(2(x1)))))) |
(115) |
|
0(4(3(4(x1)))) |
→ |
2(4(3(0(4(x1))))) |
(116) |
|
0(4(3(4(x1)))) |
→ |
3(0(2(4(4(x1))))) |
(117) |
|
0(4(3(4(x1)))) |
→ |
2(4(3(2(4(0(x1)))))) |
(118) |
|
0(4(3(4(x1)))) |
→ |
5(4(4(0(3(2(x1)))))) |
(119) |
|
0(4(3(4(x1)))) |
→ |
2(0(4(4(3(2(x1)))))) |
(120) |
|
0(4(3(4(x1)))) |
→ |
2(4(3(0(4(2(x1)))))) |
(121) |
|
0(4(3(4(x1)))) |
→ |
3(2(4(0(2(4(x1)))))) |
(122) |
|
0(4(3(4(x1)))) |
→ |
2(4(5(0(3(4(x1)))))) |
(123) |
|
0(4(3(4(x1)))) |
→ |
2(0(3(2(4(4(x1)))))) |
(124) |
|
0(4(3(4(x1)))) |
→ |
3(0(3(5(4(4(x1)))))) |
(125) |
|
1(4(3(4(x1)))) |
→ |
1(4(2(4(3(x1))))) |
(126) |
|
1(4(3(4(x1)))) |
→ |
3(2(4(2(4(1(x1)))))) |
(127) |
|
1(4(3(4(x1)))) |
→ |
4(5(4(1(3(2(x1)))))) |
(128) |
|
1(4(3(4(x1)))) |
→ |
4(1(2(4(3(2(x1)))))) |
(129) |
|
1(4(3(4(x1)))) |
→ |
4(1(3(2(4(2(x1)))))) |
(130) |
|
1(4(3(4(x1)))) |
→ |
2(4(2(4(1(3(x1)))))) |
(131) |
|
1(4(3(4(x1)))) |
→ |
1(5(4(2(4(3(x1)))))) |
(132) |
|
1(4(3(4(x1)))) |
→ |
1(4(3(5(4(3(x1)))))) |
(133) |
|
0(4(4(4(x1)))) |
→ |
0(4(4(2(4(2(x1)))))) |
(134) |
|
1(4(4(4(x1)))) |
→ |
4(1(4(2(4(2(x1)))))) |
(135) |
|
1(4(4(4(x1)))) |
→ |
4(2(1(4(2(4(x1)))))) |
(136) |
|
1(4(4(4(x1)))) |
→ |
4(5(1(4(5(4(x1)))))) |
(137) |
|
0(0(4(0(0(x1))))) |
→ |
0(0(0(2(4(0(x1)))))) |
(138) |
|
0(5(3(1(0(x1))))) |
→ |
3(5(0(3(1(0(x1)))))) |
(139) |
|
0(0(4(3(0(x1))))) |
→ |
0(0(0(2(4(3(x1)))))) |
(140) |
|
1(0(5(3(0(x1))))) |
→ |
3(2(5(0(1(0(x1)))))) |
(141) |
|
1(4(5(3(0(x1))))) |
→ |
3(5(4(0(1(5(x1)))))) |
(142) |
|
0(4(3(4(0(x1))))) |
→ |
0(4(4(3(2(0(x1)))))) |
(143) |
|
0(0(4(4(1(x1))))) |
→ |
0(0(2(4(1(4(x1)))))) |
(144) |
|
1(0(4(4(1(x1))))) |
→ |
0(2(1(4(4(1(x1)))))) |
(145) |
|
1(4(4(4(1(x1))))) |
→ |
1(4(4(1(4(2(x1)))))) |
(146) |
|
1(4(0(0(4(x1))))) |
→ |
0(1(0(2(4(4(x1)))))) |
(147) |
|
0(4(4(0(4(x1))))) |
→ |
0(4(2(4(0(4(x1)))))) |
(148) |
|
1(0(0(1(4(x1))))) |
→ |
0(1(1(0(2(4(x1)))))) |
(149) |
|
0(4(3(1(4(x1))))) |
→ |
0(4(2(4(1(3(x1)))))) |
(150) |
|
0(0(1(3(4(x1))))) |
→ |
0(0(3(2(4(1(x1)))))) |
(151) |
|
0(0(1(3(4(x1))))) |
→ |
0(0(2(4(1(3(x1)))))) |
(152) |
|
0(5(1(3(4(x1))))) |
→ |
1(0(3(5(4(1(x1)))))) |
(153) |
|
0(4(2(3(4(x1))))) |
→ |
2(4(3(0(2(4(x1)))))) |
(154) |
|
1(4(4(3(4(x1))))) |
→ |
2(4(1(3(4(4(x1)))))) |
(155) |
|
0(0(5(3(4(x1))))) |
→ |
0(3(2(5(0(4(x1)))))) |
(156) |
|
1(0(5(3(4(x1))))) |
→ |
1(0(4(5(3(2(x1)))))) |
(157) |
|
0(4(5(3(4(x1))))) |
→ |
5(4(5(4(3(0(x1)))))) |
(158) |
|
0(4(5(3(4(x1))))) |
→ |
2(4(3(5(4(0(x1)))))) |
(159) |
|
0(4(5(3(4(x1))))) |
→ |
2(0(3(5(4(4(x1)))))) |
(160) |
|
0(4(5(3(4(x1))))) |
→ |
0(2(4(3(4(5(x1)))))) |
(161) |
|
1(4(5(3(4(x1))))) |
→ |
1(5(4(2(4(3(x1)))))) |
(162) |
|
0(5(5(3(4(x1))))) |
→ |
5(4(5(3(2(0(x1)))))) |
(163) |
|
1(5(5(3(4(x1))))) |
→ |
3(5(2(4(5(1(x1)))))) |
(164) |
|
1(0(0(4(4(x1))))) |
→ |
1(0(2(4(0(4(x1)))))) |
(165) |
|
1(4(4(4(4(x1))))) |
→ |
4(2(1(4(4(4(x1)))))) |
(166) |
|
1(0(5(4(4(x1))))) |
→ |
2(4(1(0(5(4(x1)))))) |
(167) |
(w.r.t. the implicit argument filter of the reduction pair),
the
pairs
|
1#(5(5(3(4(x1))))) |
→ |
1#(x1) |
(168) |
|
1#(4(5(3(0(x1))))) |
→ |
1#(5(x1)) |
(170) |
|
1#(4(5(3(0(x1))))) |
→ |
0#(1(5(x1))) |
(171) |
|
1#(4(4(4(x1)))) |
→ |
1#(4(5(4(x1)))) |
(172) |
|
1#(4(4(4(x1)))) |
→ |
1#(4(2(4(x1)))) |
(173) |
|
1#(4(4(4(x1)))) |
→ |
1#(4(2(4(2(x1))))) |
(174) |
|
1#(4(4(4(4(x1))))) |
→ |
1#(4(4(4(x1)))) |
(175) |
|
1#(4(4(4(1(x1))))) |
→ |
1#(4(2(x1))) |
(177) |
|
1#(4(4(3(4(x1))))) |
→ |
1#(3(4(4(x1)))) |
(178) |
|
1#(4(4(1(x1)))) |
→ |
1#(4(3(2(x1)))) |
(179) |
|
1#(4(4(1(x1)))) |
→ |
1#(4(2(x1))) |
(180) |
|
1#(4(4(1(x1)))) |
→ |
1#(4(1(2(x1)))) |
(182) |
|
1#(4(4(1(x1)))) |
→ |
1#(2(x1)) |
(184) |
|
1#(4(4(1(x1)))) |
→ |
1#(2(4(2(x1)))) |
(185) |
|
1#(4(4(1(x1)))) |
→ |
1#(2(1(4(2(x1))))) |
(186) |
|
1#(4(4(0(x1)))) |
→ |
1#(x1) |
(187) |
|
1#(4(4(0(x1)))) |
→ |
1#(4(4(2(x1)))) |
(188) |
|
1#(4(4(0(x1)))) |
→ |
1#(2(4(2(4(x1))))) |
(189) |
|
1#(4(4(0(x1)))) |
→ |
1#(0(x1)) |
(190) |
|
1#(4(4(0(x1)))) |
→ |
1#(0(4(2(x1)))) |
(192) |
|
1#(4(4(0(x1)))) |
→ |
0#(4(2(x1))) |
(194) |
|
1#(4(3(4(x1)))) |
→ |
1#(x1) |
(199) |
|
1#(4(3(4(x1)))) |
→ |
1#(3(x1)) |
(203) |
|
1#(4(3(4(x1)))) |
→ |
1#(3(2(x1))) |
(204) |
|
1#(4(3(4(x1)))) |
→ |
1#(3(2(4(2(x1))))) |
(205) |
|
1#(4(3(4(x1)))) |
→ |
1#(2(4(3(2(x1))))) |
(206) |
|
1#(4(0(4(x1)))) |
→ |
0#(2(4(2(x1)))) |
(208) |
|
1#(4(0(0(x1)))) |
→ |
1#(x1) |
(209) |
|
1#(4(0(0(x1)))) |
→ |
1#(2(0(x1))) |
(210) |
|
1#(4(0(0(x1)))) |
→ |
1#(0(2(4(x1)))) |
(211) |
|
1#(4(0(0(x1)))) |
→ |
1#(0(2(4(3(x1))))) |
(212) |
|
1#(4(0(0(x1)))) |
→ |
0#(2(4(x1))) |
(213) |
|
1#(4(0(0(x1)))) |
→ |
0#(2(4(3(x1)))) |
(215) |
|
1#(4(0(0(x1)))) |
→ |
0#(1(x1)) |
(217) |
|
1#(4(0(0(4(x1))))) |
→ |
1#(0(2(4(4(x1))))) |
(220) |
|
1#(4(0(0(4(x1))))) |
→ |
0#(2(4(4(x1)))) |
(221) |
|
1#(0(5(4(4(x1))))) |
→ |
1#(0(5(4(x1)))) |
(223) |
|
1#(0(5(4(4(x1))))) |
→ |
0#(5(4(x1))) |
(224) |
|
1#(0(5(3(0(x1))))) |
→ |
1#(0(x1)) |
(227) |
|
1#(0(4(4(1(x1))))) |
→ |
1#(4(4(1(x1)))) |
(229) |
|
1#(0(0(4(x1)))) |
→ |
1#(0(3(2(x1)))) |
(231) |
|
1#(0(0(4(x1)))) |
→ |
0#(3(2(x1))) |
(232) |
|
1#(0(0(4(x1)))) |
→ |
0#(1(0(3(2(x1))))) |
(233) |
|
1#(0(0(4(4(x1))))) |
→ |
0#(4(x1)) |
(235) |
|
1#(0(0(1(4(x1))))) |
→ |
1#(1(0(2(4(x1))))) |
(237) |
|
1#(0(0(1(4(x1))))) |
→ |
1#(0(2(4(x1)))) |
(238) |
|
1#(0(0(1(4(x1))))) |
→ |
0#(2(4(x1))) |
(239) |
|
1#(0(0(0(x1)))) |
→ |
1#(0(x1)) |
(241) |
|
1#(0(0(0(x1)))) |
→ |
0#(1(0(x1))) |
(242) |
|
0#(5(5(3(4(x1))))) |
→ |
0#(x1) |
(244) |
|
0#(5(1(3(4(x1))))) |
→ |
1#(x1) |
(246) |
|
0#(4(5(3(4(x1))))) |
→ |
0#(x1) |
(249) |
|
0#(4(4(0(x1)))) |
→ |
0#(4(0(x1))) |
(255) |
|
0#(4(4(0(x1)))) |
→ |
0#(2(4(x1))) |
(256) |
|
0#(4(4(0(x1)))) |
→ |
0#(2(4(4(x1)))) |
(257) |
|
0#(4(4(0(x1)))) |
→ |
0#(0(2(4(x1)))) |
(259) |
|
0#(4(3(4(x1)))) |
→ |
0#(x1) |
(262) |
|
0#(4(3(4(x1)))) |
→ |
0#(4(x1)) |
(263) |
|
0#(4(3(4(x1)))) |
→ |
0#(4(2(x1))) |
(265) |
|
0#(4(3(4(x1)))) |
→ |
0#(3(4(x1))) |
(267) |
|
0#(4(3(4(x1)))) |
→ |
0#(3(2(x1))) |
(268) |
|
0#(4(3(4(x1)))) |
→ |
0#(2(4(x1))) |
(270) |
|
0#(4(3(1(4(x1))))) |
→ |
1#(3(x1)) |
(273) |
|
0#(4(3(0(x1)))) |
→ |
0#(3(0(x1))) |
(276) |
|
0#(4(2(3(4(x1))))) |
→ |
0#(2(4(x1))) |
(278) |
|
0#(4(0(4(x1)))) |
→ |
0#(2(4(3(x1)))) |
(280) |
|
0#(4(0(4(x1)))) |
→ |
0#(2(4(2(x1)))) |
(281) |
|
0#(4(0(4(x1)))) |
→ |
0#(0(2(4(2(x1))))) |
(282) |
|
0#(0(5(3(4(x1))))) |
→ |
0#(4(x1)) |
(283) |
|
0#(0(4(4(1(x1))))) |
→ |
1#(4(x1)) |
(285) |
|
0#(0(4(4(1(x1))))) |
→ |
0#(2(4(1(4(x1))))) |
(286) |
|
0#(0(4(3(0(x1))))) |
→ |
0#(2(4(3(x1)))) |
(288) |
|
0#(0(4(3(0(x1))))) |
→ |
0#(0(2(4(3(x1))))) |
(289) |
|
0#(0(4(0(0(x1))))) |
→ |
0#(2(4(0(x1)))) |
(291) |
|
0#(0(4(0(0(x1))))) |
→ |
0#(0(2(4(0(x1))))) |
(292) |
|
0#(0(1(3(4(x1))))) |
→ |
1#(x1) |
(294) |
|
0#(0(1(3(4(x1))))) |
→ |
1#(3(x1)) |
(295) |
|
0#(0(1(3(4(x1))))) |
→ |
0#(3(2(4(1(x1))))) |
(296) |
|
0#(0(1(3(4(x1))))) |
→ |
0#(2(4(1(3(x1))))) |
(297) |
|
0#(0(0(4(x1)))) |
→ |
0#(x1) |
(300) |
|
0#(0(0(4(x1)))) |
→ |
0#(2(4(0(x1)))) |
(301) |
and
no rules
could be deleted.
1.1.1.1 Dependency Graph Processor
The dependency pairs are split into 0
components.